The present invention relates to a method for calculating a reproduction track width of a magnetoresistive effect (MR) head and a program for calculating a reproduction track width of an MR head.
In recent years, networking of information is rapidly underway along with widespread use of personal computers. Thus, information handled includes not only conventional numeric data but also image data and so on, so that the amount of the information is dramatically increasing. In order to handle such an enormous amount of the information, a hard disk system that is high-speed, large-capacity and highly reliable is required along with a high-speed MPU.
In order to reproduce a magnetic signal recorded on a hard disk, anisotropic magnetoresistive effect heads (AMR heads) utilizing an anomalous magnetoresistive effect of a ferromagnetic material due to so-called spin-orbit interaction wherein electric resistance of a ferromagnetic thin-film layer changes depending upon an electric field are typically used.
In the AMR head, NiFe, NiFeCo, FeCo or NiCo thin film is generally used as a magneto-sensitive element. However, a magnetoresistive change rate (MR change rate) acquired is up to about two to three percent even if the NiFe thin film that has an excellent soft magnetic characteristic. For this reason, an MR head with a higher MR change rate has been demanded.
In recent years, giant magnetoresistive effect (GMR) elements such as so-called spin-valve (SV) MR elements have been proposed (for example, IEEE Trans. Magn., Vol. 30, No. 6, pp. 3801 to 3806 (1994)). In the SVMR element, a nonmagnetic conductive spacer layer is sandwiched by two ferromagnetic layers, one of the ferromagnetic layers (pinned layer) has its magnetization direction pinned by an exchange bias of an anti-ferromagnetic layer, and the other ferromagnetic layer (free layer) changes due to magnetization in an external magnetic field so as to have great change in resistance generated by an angle difference between the magnetization directions of the two ferromagnetic layers. The application of such SVMR element to a magnetic head has already been started.
In general, the magnetization direction of an MR film in the AMR head or the magnetization direction of the free layer in the SVMR head is controlled by a magnetic domain control layer to keep in a single magnetic domain state. Such magnetic domain control layer consists of magnet layers placed on both track ends of the MR film or the free layer or soft magnetic layers magnetically pinned with anti-ferromagnetic layers placed on both track ends of the MR film or the free layer, or of anti-ferromagnetic layers directly or indirectly exchange-coupled or magneto-statically coupled with the MR film or the free layer, and controls the magnetization direction in the MR film or the free layer by providing magnetic fields so as to cancel anti-magnetic fields at its track end regions. Normally, lead conductors are formed on the magnet layers or the anti-ferromagnetic layers.
A physical track width (optical track width) of the AMR head and the SVMR head (hereinafter referred to as MR heads) with such structure is defined as a space between the lead conductors on both sides of the element, a space between the magnet layers, an upside width of the element, a downside width of the element or a middle width of the element, a width of the MR film or the free layer, a width of the nonmagnetic spacer layer, a width of the pinned layer or an average width thereof.
However, the recent MR heads adopt a lead-overlaid structure wherein the lead conductors are laminated by overlapping on the MR elements, and therefore a track width contributing to actual reproduction (magnetic track width) is sometimes different from the physical track width. In such cases, it is necessary, for the sake of obtaining the actual or substantial track width, to make a measurement by reading magnetic information on thin magnetic tracks formed on the magnetic disk while moving the actually fabricated MR heads. Accordingly, it was not possible to know the substantial track width on paper or before fabricating final magnetic heads, which has been a serious problem in designing and manufacturing the MR heads.
It is therefore an object of the present invention to provide a method and a program for calculating a reproduction track width of an MR head, whereby a substantial track width of the MR head can be calculated with high accuracy and on paper.
According to the present invention, a method of calculating reproduction track width of an MR head includes a first step of subdividing at least one layer of an MR element, magnetic domain control layers of the MR element and lead conductors connected to the MR element into a plurality of polyhedral elements, based on at least data representing a shape of the at least one layer, data representing a shape of the magnetic domain control layers and data representing a shape of the lead conductors, a second step of calculating electric potentials at nodes or edges of each of the polyhedral elements at least based on resistivities of the at least one layer, the magnetic domain control layers and the lead conductors, acquiring a current density of each of the polyhedral elements based on the calculated electric potentials at the nodes or the edges, and integrating the acquired current densities to calculate an initial resistance value between terminals of the lead conductors, a third step of, in a state where a resistivity of a local block of the MR element is changed by a predetermined amount, calculating electric potentials at nodes or the edges of each of the polyhedral elements, acquiring a current density of each of the polyhedral elements based on the calculated electric potentials at the nodes or the edges, and integrating the acquired current densities to calculate a resistance value between the terminals of the lead conductors, the third step being repeated by shifting the local block with a resistivity changed by the predetermined amount, in a track width direction of the MR element, and a fourth step of obtaining a reproduction track width from the acquired initial resistance value and the acquired resistance value.
The substantial reproduction track width of the MR head is determined by the following three factors:
(a) Embedding of medium magnetic field,
(b) Sensitivity distribution of an MR film or a free layer, and
(c) Electrical reproduction track width.
The factor (a) can be easily calculated by a technique of developing a Green function in Fourier series (IEEE Trans. Magn., Vol. 34, No. 4, 1513, (1998)), and a finite element method and so on. The factor (b) can also be acquired by calculating how it is magnetized (micromagnetic simulation) according to an effective magnetic field (sum of a static magnetic field, an anisotropic magnetic field, an exchanged magnetic field and an external magnetic field) and Landau-Lifshitz-Gilbert equation (Jpn. J. Appl. Phys., 28, pp. 2485 to 2507, 1989) (IEEE Trans. Magn., Vol. 34, No. 4, pp. 1516 to 1518, (1998)). On the other hand, the factor (c) of electrical reproduction track width could not be easily acquired by a prior art, but it can now be easily calculated according to the present invention.
To be more specific, according to the present invention, each of the layer of the MR element, the magnetic domain control layers and the lead conductors is subdivided into a plurality of polyhedral elements based on the data representing the shape of the layer of the MR element itself, the data representing the shape of the magnetic domain control layers and the data representing the shape of the lead conductors. Then, electric potentials at the nodes or the edges of each polyhedral element are calculated based on the resistivity of each of these layers, and the current density of each polyhedral element is acquired from the calculated electric potentials. Then, the acquired current densities are integrated to calculate an initial resistance value between the terminals of the lead conductors. On the other hand, in the state where the resistivity in the local blocks of the MR element is changed by a predetermined amount, the electric potentials at the nodes or the edges of each polyhedral element are calculated, the current density of each polyhedral element is acquired from the calculated electric potentials, and the acquired current densities are integrated to calculate a resistance value between the terminals of the lead conductors. The local blocks are sequentially shifted in a track width direction of the MR element so as to repeatedly perform the above-mentioned calculation for calculating the resistance value, and the electrical reproduction track width is acquired from the acquired initial resistance value and resistance value. As the electrical reproduction track width of the MR head can be acquired with high accuracy, the substantial track width thereof can also be calculated with high accuracy and on paper.
It is preferred that the second step includes a step of assuming electric potentials on the nodes or the edges of each of the polyhedral elements as unknowns, a step of creating a matrix of a finite element method on the nodes or the edges in accordance with a weighted residual equation based on a polyhedral element volume coordinate and a resistivity of each of the polyhedral elements, a step of creating a column vector by providing a fixed boundary condition to upper surfaces of the lead conductors, and a step of solving equations of the matrix and the column vector to calculate the electric potential at each node or edge.
It is also preferred that the second step further includes a step of acquiring a current density of each of the polyhedral elements by calculating a strength of the electric field of each of the polyhedral elements from the calculated electric potentials at the nodes or the edges, a step of acquiring a current value between the terminals of the lead conductors by integrating the acquired current densities of the polyhedral elements, and a step of calculating the initial resistance value from the acquired current value and a potential difference between the terminals of the lead conductors.
It is further preferred that the third step includes a step of assuming electric potentials on the nodes or the edges of each of the polyhedral elements as unknowns, a step of creating a matrix of a finite element method on the nodes or the edges in accordance with a weighted residual equation based on a polyhedral element volume coordinate and a resistivity of each of the polyhedral elements, a step of creating a column vector by providing a fixed boundary condition to upper surfaces of the lead conductors, and a step of solving equations of the matrix and the column vector to calculate the electric potential at each node or edge.
It Is also preferred that the third step further includes a step of acquiring a current density of each of the polyhedral elements by calculating a strength of the electric field of each of the polyhedral elements from the calculated electric potentials at the nodes or the edges, a step of acquiring a current value between the terminals of the lead conductors by integrating the acquired current densities of the polyhedral elements, and a step of calculating the resistance value from the acquired current value and a potential difference between the terminals of the lead conductors.
It is preferred that the fourth step includes a step of acquiring the reproduction track width from a characteristic representing a relationship between a position in the track width direction and a difference between the resistance value and the initial resistance value of the local block corresponding to the position.
According to the present invention, furthermore, a program for calculating a reproduction track width of an MR head, causing a computer to function as a first means for subdividing at least one layer of an MR element, magnetic domain control layers of the MR element and lead conductors connected to the MR element into a plurality of polyhedral elements, based on at least data representing a shape of the at least one layer, data representing a shape of the magnetic domain control layers and data representing a shape of the lead conductors, a second means for of calculating electric potentials at nodes or edges of each of the polyhedral elements at least based on resistivities of the at least one layer, the magnetic domain control layers and the lead conductors, acquiring a current density of each of the polyhedral elements based on the calculated electric potentials at the nodes or the edges, and integrating the acquired current densities to calculate an initial resistance value between terminals of the lead conductors, and a third means for, in a state where a resistivity of a local block of the MR element is changed by a predetermined amount, calculating electric potentials at nodes or the edges of each of the polyhedral elements, acquiring a current density of each of the polyhedral elements based on the calculated electric potentials at the nodes or the edges, and integrating the acquired current densities to calculate a resistance value between the terminals of the lead conductors, functions of the third means being repeated by shifting the local block with a resistivity changed by the predetermined amount, in a track width direction of the MR element, whereby a reproduction track width is obtained from the acquired initial resistance value and the acquired resistance value.
Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings.